Course Information

This course has two (related) parts. The first half of the course will be devoted to the study of fields and Galois Theory. Then we shall concentrate on extension of commutative rings. Below are the topics we shall cover:

* Field Extensions

* Normal and Separable Extensions

* Fundamental Theorem of Galois Theory

* Cyclotomic Extensions

* Norm and Trace

* Hilbert's 90 and Abelian Kummer Theory

* Noetherian Rings

* Integral Extensions

* Localization

* Discrete Valuation Rings and Dedekind Domains

For more information: (Syllabus)

Notes

Hand-written lecture notes are HERE

Typed lecture notes are HERE (these are being typed as the semester continues)

Homeworks

* HW 1

* HW 2

* HW 3

* HW 4

* HW 5